The Valar aren't perfect either, and can make mistakes. Also remember, in the beginning, Melkor was stronger than all other Valar combined. The Valar did intervene swiftly after discovering the Elves when they invited them to Aman to protect them from Melkor. While that may seem an obvious thing to do, in the long term it might not actually have been the best idea. The first mistake might have been creating Aman at all, and living apart from Middle Earth. The second mistake might have been inviting the Elves to leave Middle Earth and come live with them there. It is implied that, counterintuitive as it might seem, in the long term it might have been better for the Elves to have stayed in Middle Earth. Maybe that might have prevented the corruption of men (humans) in the first place, among other things.

I keep saying "might," because it's impossible to know for sure. The string of causation is impossibly vast and complex. The point is that even something which seems obviously the right thing to do might not actually be.

But really your question can basically be boiled down to, "Why does evil and suffering exist at all?"

If God/Eru Ilúvatar is so all-good, all-knowing, and all-powerful, why create a being like Melkor in the first place? Why even permit the existence of anything that has the potential to go wrong?

That's just a mystery. Nobody, not even the Valar, knows that. There is only the assurance that no matter how terrible and hopeless things may seem, there is no evil or suffering for which there won't ultimately be justice, because everything has its source in Eru:

"Thou, Melkor, shalt see that no theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite. For he that attempteth this shall prove but mine instrument in the devising of things more wonderful, which he himself hath not imagined."

Also when Feanor rebels against the Valar and rejects their summons:

"When the messengers declared to Manwë the answers of Fëanor to his heralds, Manwë wept and bowed his head. But at that last word of Fëanor: that at the least the Noldor should do deeds to live in song for ever, he raised his head, as one that hears a voice far off, and he said: ‘So shall it be! Dear-bought those songs shall be accounted, and yet shall be well-bought. For the price could be no other. Thus even as Eru spoke to us shall beauty not before conceived be brought into Eä, and evil yet be good to have been.'

But Mandos said: ‘And yet remain evil. To me shall Fëanor come soon.’"